Subnormalizers and the degree of nilpotence in finite groups
HTML articles powered by AMS MathViewer
- by Pietro Gheri
- Proc. Amer. Math. Soc. 149 (2021), 2739-2744
- DOI: https://doi.org/10.1090/proc/15080
- Published electronically: April 22, 2021
- PDF | Request permission
Abstract:
We present a CFSG-free proof of the fact that the degree of nilpotence of a finite nonnilpotent group is less than $1/2$.References
- Carlo Casolo, Subnormalizers in finite groups, Comm. Algebra 18 (1990), no. 11, 3791–3818. MR 1068623, DOI 10.1080/00927879008824110
- Carlo Casolo, On the subnormalizer of a $p$-subgroup, J. Pure Appl. Algebra 77 (1992), no. 3, 231–238. MR 1154702, DOI 10.1016/0022-4049(92)90139-7
- R. M. Guralnick and J. S. Wilson, The probability of generating a finite soluble group, Proc. London Math. Soc. (3) 81 (2000), no. 2, 405–427. MR 1770615, DOI 10.1112/S0024611500012569
- W. H. Gustafson, What is the probability that two group elements commute?, Amer. Math. Monthly 80 (1973), 1031–1034. MR 327901, DOI 10.2307/2318778
- John C. Lennox and Stewart E. Stonehewer, Subnormal subgroups of groups, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1987. Oxford Science Publications. MR 902587
Bibliographic Information
- Pietro Gheri
- Affiliation: Dipartimento di Matematica e Informatica “U. Dini”, Università degli Studi di Firenze, viale Morgagni 67/a, 50134 Firenze, Italy
- Email: pietro.gheri@unifi.it
- Received by editor(s): January 30, 2020
- Received by editor(s) in revised form: February 12, 2020
- Published electronically: April 22, 2021
- Additional Notes: This work was partially funded by the Istituto Nazionale di Alta Matematica “Francesco Severi” (Indam)
- Communicated by: Martin Liebeck
- © Copyright 2021 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 149 (2021), 2739-2744
- MSC (2020): Primary 20D15, 20P05
- DOI: https://doi.org/10.1090/proc/15080
- MathSciNet review: 4257789